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Find the nature of the turning points of the graph given by the equation x^4 +(8/3)*x^3 -2x^2 -8x +177 (6 marks)

(1 mark) Differentiate equation in the question: 4x 3 +8x 2 -4x-8(1 mark) Equate this to zero: (x-1)(x+1)(x+2)=0(1 mark) Find turning points (roots of above equation): x=1,-1,-2(1 mark) Differentiate again: ...
EB
Answered by Elizabeth B. • Maths tutor
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show that y = (kx^2-1)/(kx^2+1) has exactly one stationary point when k is non-zero.

Stationary points are found by considering the points at which the gradient of the function equal zero. For the above, you need to employ the quotient rule, since both numerator and denominator are f(x), to ...
RM
Answered by Rob M. • Maths tutor
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A ball is projected vertically upwards from the ground with speed 21 ms^–1. The ball moves freely under gravity once projected. What is the greatest height reached by the ball?

Set out information given in question, and taking the upward direction to be positive: s (displacement) = ?, u (initial speed) = 21ms -1 , v (final speed at maximum height) = 0ms -1 , a (acceleration when fa...
SS
Answered by Shruti S. • Maths tutor
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Solve 7x + 6 > 1 + 2x

7x + 6 > 1 + 2xFirst, we collect the like terms so we move all the x's to one side and all the integers to the other:5x > -5Then we divide by 5 on each side to find what just x will be.Therefore, x &gt...
JZ
Answered by Juliet Z. • Maths tutor
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Let C : x^2-4x+2k be a parabola, with vertex m. By taking derivatives or otherwise discuss, as k varies, the coordinates of m and, accordingly, the number of solutions of the equation x^2-4x+2k=0. Illustrate your work with graphs

Write y=x 2 -4x+2k. And m:= (x m , y m ) for the coordinates of our vertex. We deduce that x m is exactly the value of x for which y'=2x-4=0, because m is a minimum point of y. By solving y'=0, we get x=2=x ...
MV
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